Average Error: 0.0 → 0.0
Time: 19.2s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\mathsf{fma}\left(y, z - x, x\right)\]
x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(y, z - x, x\right)
double f(double x, double y, double z) {
        double r914533 = x;
        double r914534 = y;
        double r914535 = z;
        double r914536 = r914535 - r914533;
        double r914537 = r914534 * r914536;
        double r914538 = r914533 + r914537;
        return r914538;
}
↓
double f(double x, double y, double z) {
        double r914539 = y;
        double r914540 = z;
        double r914541 = x;
        double r914542 = r914540 - r914541;
        double r914543 = fma(r914539, r914542, r914541);
        return r914543;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x + y \cdot \left(z - x\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, z - x, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, z - x, x\right)\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))